We study two-dimensional flow in a layered heterogeneous medium composed of two materials whose hydraulic properties and spatial distribution are known statistically but are otherwise uncertain. Our analysis relies on the composite media theory, which explicitly accounts for the separate effects of material and geometric uncertainty on statistical moments of head and flux. Flow parallel and perpendicular to the layering in a composite layered medium is considered. The hydraulic conductivity of each material is lognormally distributed with a much higher mean in one material than in the other. The hydraulic conductivities of points within different materials are uncorrelated. The location of the internal boundary between the two contrasting materials is usually distributed randomly with given mean and variance. We solve the equations for (ensemble) moments of hydraulic head and flux and analyse the impact of unknown geometry of materials on the distribution of head variance.